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 A235391 Expansion of 2 / (2 - x / sqrt(1 - 4*x)). 1
 1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895, 322037615290, 1305256267511, 5293166568270, 21475362822956, 87166344495561, 353933533606927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1 / (1 - x / (1 - x / (1 - 2*x / (1 - x / (2 - 3*x / (1 - 2*x / (3 - 4*x / ... ))))))). D-finite with recurrence: 0 = (4*n + 6) * a(n) - (17*n + 27) * a(n+1) + (24*n + 42) * a(n+2) - (9*n + 21) * a(n+3) + (n + 3) * a(n+4). - Sign flipped by R. J. Mathar, Feb 16 2020 0 = a(n) * (16*a(n+1) - 74*a(n+2) + 120*a(n+3) - 66*a(n+4) + 10*a(n+5))+ a(n+1) * (-62*a(n+1) + 361*a(n+2) - 480*a(n+3) + 265*a(n+4) - 41*a(n+5)) + a(n+2) * (-342*a(n+2) + 615*a(n+3) - 335*a(n+4) + 54*a(n+5)) + a(n+3) * (-90*a(n+3) + 75*a(n+4) - 15*a(n+5)) + a(n+4) * (-3*a(n+4) + a(n+5)). a(n) = A129775(n) if n>0. HANKEL transform is A000012. INVERT transform is A073525. EXAMPLE G.f. = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 78*x^5 + 298*x^6 + 1157*x^7 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 2 / (2 - x - x / Sqrt[1 - 4 x]), {x, 0, n}] PROG (PARI) {a(n) = if( n<0, 0, polcoeff( 2 / (2 - x - x / sqrt(1 - 4*x + x * O(x^n))), n))} (MAGMA) m:=25; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!(2/( 2-x - x/Sqrt(1-4*x)))); // G. C. Greubel, Aug 07 2018 CROSSREFS Cf. A000012, A073525, A129775. Sequence in context: A277221 A129776 A129775 * A254316 A279562 A054515 Adjacent sequences:  A235388 A235389 A235390 * A235392 A235393 A235394 KEYWORD nonn AUTHOR Michael Somos, Jan 09 2014 STATUS approved

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Last modified December 2 16:17 EST 2021. Contains 349445 sequences. (Running on oeis4.)